The art is replete with games, puzzles, educational toys, models and various mathematical recreations involving the assembly of geometric pieces into some type of pattern or structure. A considerable body of literature on the subject exists and continues to grow with the issuance of new patents and publications for educators, students, and hobbyists. An excellent review and compilation of the art may be found in Puzzle Craft by Stewart T. Coffin (1985; published by Stewart Coffin, 79 Old Sudbury Road, Lincoln, Mass. 01773). Another extensive survey may be found in Puzzles Old & New, How To Make and Solve Them by Jerry Slocum and Jack Botermans (1986, Plenary Publication International (Europe) bv, De Meern, The Netherlands and ADM International bv, Amsterdam, The Netherlands).
Even a cursory review of the literature will indicate that many of the puzzles which are most popular involve the combining or arranging of a group of pieces in some particular way or ways which constitute the solution of the puzzle. The present invention, although it has applications in education, architecture and design in general can probably best be understood in the context of such "combinatorial puzzles".
A basic underlying concept of the present invention involves component pieces and accessories having dimensions scaled by values in the geometrical and additive series of Phi, thus demonstrating the proportion known as the "Golden Section". The proportion derived from the ratio Phi has been used in the art and architecture for the creation of proportional form and may be expressed as: ##EQU1## which is equal to 1.618 . . . . Much has been written of the golden section, and a particularly valuable publication of the subject is The Geometry of Art and Life by Matila Ghyke, Dover Publications, Inc., New York, N.Y. 10014 (1977).
For present purposes, it is sufficient to note that the number or ratio, or proportion Phi has been designated .phi. and has long been known to have properties as remarkable in their way as the better known number .pi.. For example, concerning the geometrical and additive series: ##EQU2##
There is at least one puzzle known in the art which involves dissimilar pieces each having a side length related to powers of the golden section, the pieces being combinable to form various polygons and other geometric figures. This puzzle is disclosed in U.S. Pat. No. 4,343,471, Pentagonal Puzzle, issued Aug. 10, 1982 to Calvert.
It is a primary object of this invention to utilize the additive and geometrical properties of the Golden Section in a challenging mathematical recreation.
Another object is to provide a geometric puzzle which is playable at different degrees of difficulty.
Still another object is to aid the teaching of mathematical relationships and the understanding and appreciation of art.
A further object is to provide a puzzle which when solved expresses the symmetry of geometric form and color.